In the conversation taking place on a bus, Trump tells Billy Bush – a cousin of George and Jeb Bush who was the then host of Access Hollywood – about his approach with women as they prepare to meet a soap opera star for a segment.

The newly married Trump reminisces about making a pass at a married woman. “I moved on her and I failed, I’ll admit it … I did try and fuck her. She was married.” The Republican nominee goes on to describe his efforts at seduction by saying: “I moved on her like a bitch but I couldn’t get there and she was married …

“I am automatically attracted to beautiful women. I just start kissing them. It’s like a magnet. Just kiss, I don’t even wait … and when you’re a star they let you do it. You can do anything.”

Bush banters with Trump and eggs him on before the businessman says: “Grab them by the pussy. You can do anything.”

The comments, made on live microphone, were revealed by the Washington Post on Friday.

Hillary Clinton, the Democratic candidate for president, said via Twitter: “This is horrific. We cannot allow this man to become president.”

Trump initially dismissed the vulgar bragging as “locker room banter, a private conversation that took place many years ago”. He added: “Bill Clinton has said far worse to me on the golf course – not even close. I apologize if anyone was offended.”

But as one Republican after another lined up to condemn the lewd banter – including the Speaker of the House, Paul Ryan, who cancelled a joint campaign appearance – Trump was forced to prepare a fuller apology.

In a 90-second video released after midnight, Trump said: “Anyone who knows me knows these words don’t reflect who I am. I said it. I am wrong. I apologize.

“I’ve never said I am a perfect person, nor pretended to be someone that I am not. I’ve said and done things I regret and the words released today on this more than decade-old video are one of them.”

However, Trump characteristically tried to turn to his advantage a situation brought about by his own outrageous behaviour – by pointing the finger at someone else.

He continued: “I’ve said some foolish things but there is a big difference between the words and actions of other people. Bill Clinton has actually abused women and Hillary has bullied, attacked, shamed and intimidated his victims. We will discuss this more in the coming days. See you at the debate on Sunday.”

The latest controversy sent Trump’s party into yet another frenzy, with Republican lawmakers having to once again issue swift condemnations of their own standard bearer.

Ryan, the top-ranking Republican in Washington, said he was “sickened” by the recording and that Trump would no longer appear at what would have been their first campaign event together in Ryan’s home state of Wisconsin on Saturday. Trump confirmed that his running mate, the Indiana governor, Mike Pence, would take his place at the Republican county festival.

Mitch McConnell, the Senate majority leader, said Trump’s remarks were “unacceptable in any circumstance”.

“As the father of three daughters, I strongly believe that Trump needs to apologize directly to women and girls everywhere, and take full responsibility for the utter lack of respect for women shown in his comments on that tape,” McConnell said.

But neither of the Republican leaders withdrew their endorsements of Trump.

Some members of Trump’s party, however, signaled any patience they might have had was gone, including a group from Utah where Trump has struggled to find support among a heavily Mormon population.

Gary Herbert, the Republican governor of Utah, wrote on Twitter that Trump’s remarks were “beyond offensive and despicable”.

“While I cannot vote for Hillary Clinton, I will not vote for Trump,” he said.

Jason Chaffetz, the Republican congressman who chairs the House committee that is investigating Clinton’s use of a private email server, also withdrew his support.

“I’m out – I can no longer in good conscience endorse this person for president,” Chaffetz told a Fox television affiliate. “It is some of the most abhorrent and offensive comments that you can possibly imagine.” He said he could no longer look his 15-year-old daughter or wife in the eye while backing Trump. On CNN, Chaffetz claimed Trump had only “apologised for getting caught”.

The former Utah governor Jon Huntsman, who ran unsuccessfully for the Republican nomination in 2012, said Trump should drop out of the race. Mitt Romney, who in 2012 became the first Mormon presidential nominee of a major party, said: “Hitting on married women? Condoning assault? Such vile degradations demean our wives and daughters and corrupt America’s face to the world.”

Mike Lee, a Utah senator well regarded across the conservative movement who had already declined to endorse Trump because of his attacks on Ted Cruz, joined a chorus of voices calling on Trump to step aside.

“You, sir, are a distraction. Your conduct is a distraction. This can’t continue. It’s time for us not to settle. It’s time for us to expect more.”

There was some milder criticism from vulnerable senators whose re-election bids will determine whether Republicans maintain their precarious control over the US Senate in November.

Marco Rubio, the Florida senator who sparred bitterly with Trump in the Republican presidential primary, said the comments “were vulgar, egregious and impossible to justify”.

“No one should ever talk about any woman in those terms, even in private,” said Rubio, who nonetheless plans to vote for Trump next month.

Senator John McCain of Arizona said there were “no excuses for Donald Trump’s offensive and demeaning comments”.

“No woman should ever be victimized by this kind of inappropriate behavior,” the 2008 Republican presidential nominee said in a statement. “He alone bears the burden of his conduct and alone should suffer the consequences.”

But McCain similarly declined to rescind his endorsement of Trump.

There were similar statements from senators Rob Portman of Ohio, Richard Burr of North Carolina, Pat Toomey of Pennsylvania and Kelly Ayotte of New Hampshire: Trump’s “offensive and unacceptable comments” deserved rebuke but not quite retreat.

Trump – who got his start in political life by spreading the lie that Barack Obama was not born in the US – has a history of offensive statements towards women, minorities, foreigners and non-white constituents.

He launched his campaign in June 2015 by suggesting that Mexico was deliberately sending rapists across the border into the US. He has attacked the Muslim parents of a soldier killed in Iraq; accused the federal judge Gonzalo Curiel of being biased because of his Mexican background; declared that McCain, a survivor of torture, was not a war hero because he was captured; and called for a blanket ban on all Muslims entering the country.

Regarding women, Trump insinuated that the Fox News anchor Megyn Kelly asked him tough questions in the first primary debate because she was menstruating. He described former rival Carly Fiorina as being unattractive. In the first presidential debate in September, Trump was criticized by Clinton for calling a Venezuelan winner of the Miss Universe competition “Miss Piggy” and “Miss Housekeeping”. In response, he used Twitter to falsely claim that the woman, Alicia Machado, had made a sex tape.

In July, Cruz withheld his support for Trump and urged fellow Republicans to “vote your conscience”, but two weeks ago, he gave the candidate his endorsement. After the release of the tape, Cruz’s condemnation failed to go so far as withdrawing that endorsement.